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IGCSE 数学 0580 Paper 3（Core）模拟卷｜104 分・2 小时・可用计算机
练习卷 · IGCSE 数学 0580 Paper 3（Core）
IGCSE 数学 0580 Paper 3（Core）模拟卷：51 题共 104 分、2 小时、可用计算机，涵盖数字运算、代数、图形与空间、数据与概率四大范畴，每题附答案与简明步骤，方便家长即时对答案，题目版与答案版 PDF 可即时下载。
卷面资料 年级：IGCSE（Core） ｜ 科目：数学 ｜ 时限：120 分钟 ｜ 总分：104 分 ｜ 题数：51
甲部：数字（26 分）
全部作答，可使用计算机。
| # | 题目 | 答案与评分要点 |
|---|---|---|
| 1 | Work out 3.6 × 2.5. | 3 × 2.5 = 7.5 and 0.6 × 2.5 = 1.5, so 7.5 + 1.5 = 9 |
| 2 | A concert ticket costs $480. The price then increases by 15%%. Work out the new price. | 15% of $480 = $72, so $480 + $72 = $552 |
| 3 | A car travels 156 km in 2.4 hours. Work out its average speed in km/h. | 156 / 2.4 = 65 km/h |
| 4 | Convert 4 500 mm to metres. | 1 m = 1 000 mm, so 4 500 / 1 000 = 4.5 m |
| 5 | Write 0.625 as a fraction in its simplest form. | 625/1000 = 5/8 |
| 6 | Find 35%% of 260. | 10% = 26, 30% = 78, 5% = 13, so 35% = 91 |
| 7 | Share $560 in the ratio 3 : 4 : 7. | 3 + 4 + 7 = 14 parts, $560 / 14 = $40, so $120, $160 and $280 |
| 8 | Work out 2.7² − 1.44. | 2.7 × 2.7 = 7.29, then 7.29 – 1.44 = 5.85 |
| 9 | Write 3.6472 correct to 3 significant figures. | The 4th significant figure is 7, so round up: 3.65 |
| 10 | In a sale a bag costing $240 is reduced by 20%%. Work out the sale price. | 20% of $240 = $48, so $240 – $48 = $192 |
| 11 | Write 0.00042 in standard form. | 0.00042 = 4.2 × 10^-4 |
| 12 | Find the lowest common multiple (LCM) of 24 and 36. | 24 = 2³ × 3 and 36 = 2² × 3², so LCM = 2³ × 3² = 72 |
| 13 | Work out 3/4 × 2/9. Give your answer in its simplest form. | 3/4 × 2/9 = 6/36 = 1/6 |
| 14 | A recipe for 6 people needs 450 g of flour. Work out the amount of flour needed for 15 people. | 450 / 6 = 75 g per person, and 75 × 15 = 1125 g |
| 15 | $2 000 is invested at 4.5%% simple interest per year. Work out the interest after 3 years. | 2 000 × 0.045 × 3 = $270 |
| 16 | A map has a scale of 1 : 50 000. A road is 7.2 cm long on the map. Work out the real length of the road in kilometres. | 7.2 × 50 000 = 360 000 cm = 3.6 km |
乙部：代数（26 分）
化简及解方程，须列出步骤。
| # | 题目 | 答案与评分要点 |
|---|---|---|
| 17 | Simplify 7x – 3y + 2x + 5y. | 7x + 2x = 9x and -3y + 5y = 2y, so 9x + 2y |
| 18 | Expand 4(3x – 2). | 4 × 3x = 12x and 4 × (-2) = -8, so 12x – 8 |
| 19 | Factorise 6x + 9y. | The highest common factor is 3, so 3(2x + 3y) |
| 20 | Solve 5x – 8 = 42. | 5x = 42 + 8 = 50, so × = 10 |
| 21 | Solve 3(x + 4) = 2x + 19. | 3x + 12 = 2x + 19, so × = 19 – 12 = 7 |
| 22 | The first four terms of a sequence are 5, 8, 11, 14. (a) Find the 20th term. (b) Write down an expression for the nth term. | (a) The difference is 3, so the 20th term is 3 × 20 + 2 = 62. (b) nth term = 3n + 2 |
| 23 | v = u + at. Work out v when u = 12, a = 3.5 and t = 8. | 3.5 × 8 = 28, so v = 12 + 28 = 40 |
| 24 | Make t the subject of the formula s = (u + v)t / 2. | 2s = (u + v)t, so t = 2s / (u + v) |
| 25 | Work out the value of y when × = -2, given y = 3x² – 2x. | 3 × 4 = 12 and -2 × (-2) = +4, so y = 12 + 4 = 16 |
| 26 | Solve x² = 49. | Taking the square root gives × = 7 or × = -7 |
| 27 | Expand and simplify (x + 5)(x – 3). | x² – 3x + 5x – 15 = x² + 2x – 15 |
| 28 | Solve the inequality 4x + 3 ≤ 27. | 4x ≤ 24, so × ≤ 6 |
丙部：图形与空间（30 分）
图形未必按比例绸画。
| # | 题目 | 答案与评分要点 |
|---|---|---|
| 29 | Work out the sum of the interior angles of a hexagon. | (6 – 2) × 180° = 720° |
| 30 | Work out the size of each exterior angle of a regular octagon. | 360° / 8 = 45° |
| 31 | A circle has radius 7.5 cm. Work out its area. Use π = 3.142. | 3.142 × 7.5 × 7.5 = 176.7 cm² |
| 32 | A cylinder has radius 4 cm and height 10 cm. Work out its volume. Use π = 3.142. | 3.142 × 16 × 10 = 502.72 cm³ |
| 33 | A prism has a constant cross-section of area 12 cm² and a length of 15 cm. Work out its volume. | 12 × 15 = 180 cm³ |
| 34 | A shape is enlarged by scale factor 2.5. Work out the area scale factor. | 2.5 × 2.5 = 6.25 |
| 35 | Two triangles are similar. The smaller triangle has area 20 cm² and the smaller of two corresponding sides is 6 cm. The larger corresponding side is 9 cm. Work out the area of the larger triangle. | Length factor 9/6 = 1.5, so area factor 1.5² = 2.25, and 20 × 2.25 = 45.0 cm² |
| 36 | A right-angled triangle has two shorter sides of length 9 cm and 12 cm. Work out the length of the hypotenuse. | 9² + 12² = 81 + 144 = 225, and the square root of 225 is 15.0 cm |
| 37 | In a right-angled triangle the hypotenuse is 13 cm and the side opposite angle θ is 5 cm. Work out the size of angle θ, correct to 1 decimal place. | sinθ = 5/13 = 0.3846, so θ = 22.6° |
| 38 | A ship sails on a bearing of 065°. It then turns 130° clockwise. Write down its new bearing. | 65 + 130 = 195° |
| 39 | A trapezium has parallel sides of length 8 cm and 14 cm and a height of 6 cm. Work out its area. | (8 + 14) / 2 = 11, and 11 × 6 = 66.0 cm² |
| 40 | A sector of a circle has radius 9 cm and angle 140°. Work out the length of its arc. Use π = 3.142. | 140/360 × 2 × 3.142 × 9 = 21.99 cm |
| 41 | A sphere has radius 3 cm. Work out its volume. Use π = 3.142. | 4/3 × 3.142 × 27 = 113.112 cm³ |
丁部：数据与概率（22 分）
概率以最简分数作答。
| # | 题目 | 答案与评分要点 |
|---|---|---|
| 42 | The number of goals scored in five matches were 14, 18, 9, 21 and 13. Work out the mean. | (14 + 18 + 9 + 21 + 13) / 5 = 75 / 5 = 15 |
| 43 | Here are seven test scores: 4, 6, 6, 8, 11, 13, 15. Write down (a) the median, (b) the mode, (c) the range. | (a) the middle value is 8 (b) mode = 6 (c) 15 – 4 = 11 |
| 44 | A bag contains 3 red, 5 green and 4 blue counters. One counter is taken at random. Work out the probability that it is not blue. | 8 of the 12 counters are not blue, so P = 8/12 = 2/3 |
| 45 | A fair dice is rolled once. Work out the probability of scoring more than 4. | The scores 5 and 6 work, so P = 2/6 = 1/3 |
| 46 | In a pie chart 36 out of 90 students chose football. Work out the angle of that sector. | 36/90 × 360° = 144.0° |
| 47 | A spinner landed on 6 forty-six times in 200 spins. (a) Estimate the probability of landing on 6. (b) Work out how many times it is expected to land on 6 in 500 spins. | (a) 46/200 = 0.23 (b) 0.23 × 500 = 115 |
| 48 | Two independent events have probabilities 0.4 and 0.5. Work out the probability that both events happen. | 0.4 × 0.5 = 0.2 |
| 49 | The mean of five numbers is 12. Four of the numbers are 9, 14, 11 and 13. Find the fifth number. | Total = 5 × 12 = 60, and 60 – 47 = 13 |
| 50 | The probability that a train is late is 0.62. Work out the probability that it is not late. | 1 – 0.62 = 0.38 |
| 51 | The smallest value in a data set is 3.2 and the largest value is 9.8. Write down the range. | 9.8 – 3.2 = 6.6 |
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